Enteroviruses: Dose Response Models

Enteroviruses

Author: Yin Huang If you want to download this chapter in pdf format, please click here

General overview

Enterovirus, a kind of small (30 nm), nonenveloped, single-stranded RNA viruses, belongs to the family Picornaviridae. While most of the enterovirus infections are relatively mild and result in complete recovery of the patient, they can also cause severe and fatal diseases such as meningitis, encephalitis, myocarditis, neonatal sepsis, and polio. Infection occurs mainly via fecal-oral transmission and less commonly by respiratory droplets. While no known non-human reservoirs have been identified, water-borne, foodborne, and blood-borne transmissions have been reported (Stalkup and Chilukuri 2002).

---

Summary Data

Cliver (1981) challenged pigs with Porcine enterovirus type 3 and 7 via oral exposure route.

Table 3.1. Summary of the enterovirus data and best fits Experiment number Reference Host type/pathogen strain Route/number of doses Dose units Response Best-fit modela Optimized parameters ID50 1 Cliver, 1981 pigs/ Porcine enterovirus type 3 oral/3 pfu infection Exponential k = 2.96E-04 2340.15 2* Cliver, 1981 pigs/ Porcine enterovirus type 7 oral/3 pfu infection Exponential k = 3.75E-03 185.10

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50 63* pig porcine, PE7-05i oral 3 pfu infection exponential k = 3.74E-03 1.85E+02 62 pig porcine, PE3-ECPO-6 oral 3 pfu infection exponential k = 2.96E-04 2.34E+03 *This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

^*Recommended Model

It is recommended that experiment 1 should be used as the best dose-response model. A more virulent strain in experiment 1 can be more meaningful for emergency preparedness.

a:

---

Optimization Output for experiment 63

pigs/ Porcine enterovirus type 7 Dose infected Non-infected Total 250 4 2 6 250 3 3 6 1000 5 0 5

Goodness of fit and model selection Model Deviance Δ Degrees of freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 0.614 -5.49e-05 2 3.84 1 5.99 0.736 Beta Poisson 0.614 1 3.84 0.433 Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

Optimized k parameter for the exponential model, from 10000 bootstrap iterations Parameter MLE estimate Percentiles 0.5% 2.5% 5% 95% 97.5% 99.5% k 3.74E-03 1.83E-03 2.19E-03 2.19E-03 5.62E-03 5.62E-03 5.62E-03 ID50/LD50/ETC* 1.85E+02 1.23E+02 1.23E+02 1.23E+02 3.16E+02 3.16E+02 3.79E+02 *Not a parameter of the exponential model; however, it facilitates comparison with other models.

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

Optimization Output for experiment 62

Pigs/ Porcine enterovirus type 3 Strain model data Dose infected Non-infected Total 100 0 3 3 250 0 6 6 1000 2 4 6

Goodness of fit and model selection Model Deviance Δ Degrees of freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 1.24 -0.000314 2 3.84 1 5.99 0.537 Beta Poisson 1.24 1 3.84 0.265 Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

Optimized k parameter for the exponential model, from 10000 bootstrap iterations Parameter MLE estimate Percentiles 0.5% 2.5% 5% 95% 97.5% 99.5% k 2.96E-04 2.40E-17 2.40E-17 2.40E-17 7.19E-04 7.19E-04 1.02E-03 ID50/LD50/ETC* 2.34E+03 6.77E+02 9.64E+02 9.64E+02 2.89E+16 2.89E+16 2.89E+16 *Not a parameter of the exponential model; however, it facilitates comparison with other models.

Parameter histogram for exponential model (uncertainty of the parameter)

Exponential model plot, with confidence bounds around optimized model

Optimized Models and Fitting Analyses

Optimization Output for experiment 1

Table 3.2. Pigs/ Porcine enterovirus type 3 Strain model data Dose Infected Non-infected Total 1.00E+02 0 3 3 2.50E+02 0 6 6 1.00E+03 2 4 6 Cliver, 1981.

Table 3.3: Goodness of fit and model selection Model Deviance Δ Degrees of Freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 1.24 3.00E-04 2 3.84 0.986 5.99 0.537 Beta Poisson 1.24 1 3.84 0.265 Exponential is best fitting model

Table 3.4 Optimized parameters for the best fitting (Exponential), obtained from 10,000 bootstrap iterations Parameter or value MLE Estimate Percentiles 0.50% 2.5% 5% 95% 97.5% 99.5% k 2.96E-04 2.40E-17 2.40E-17 2.40E-17 7.19E-04 7.19E-04 1.03E-03 LD50 (spores) 2340.15 676.57 963.88 963.88 2.89E+16 2.89E+16 2.89E+16

Figure 3.1 Parameter histogram for exponential model (uncertainty of the parameter)

Figure 3.2 Exponential model plot, with confidence bounds around optimized model

---

Optimization Output for experiment 2

Table 3.5 pigs/ Porcine enterovirus type 7 Dose Infected Non-infected Total 2.50E+02 4 2 6 2.50E+02 3 3 6 1.00E+03 5 0 5 Cliver, 1981.

Table 3.6: Goodness of fit and model selection Model Deviance Δ Degrees of Freedom χ20.95,1 p-value χ20.95,m-k p-value Exponential 0.61 1.00E-04 2 3.84 0.994 5.99 0.736 Beta Poisson 0.61 1 3.84 0.433 Exponential is best fitting model

Table 3.7 Optimized parameters for the best fitting (exponential), obtained from 10,000 bootstrap iterations Parameter or value MLE Estimate Percentiles 0.50% 2.5% 5% 95% 97.5% 99.5% k 3.75E-03 1.83E-03 2.19E-03 2.19E-03 5.62E-03 5.62E-03 5.62E-03 LD50 (spores) 185.10 123.36 123.36 123.36 316.32 316.32 378.96

Figure 3.3 Parameter histogram for exponential model (uncertainty of the parameter)

Figure 3.4 Exponential model plot, with confidence bounds around optimized model

---

Summary

The different LD₅₀ for these two experiments indicates various virulence between pathogen strains.

---

References

Cliver, D. O. (1981). "Experimental infection by waterborne enteroviruses." Journal of Food Protection 44: 861-865.

Stalkup, J. R. and S. Chilukuri (2002). "Enterovirus infections: a review of clinical presentation, diagnosis, and treatment." Dermatologic clinics 20(2): 217-223.